{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Merging Optics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from optiland import optic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Singlet(optic.Optic):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "\n",
    "        # add surfaces\n",
    "        self.add_surface(index=0, thickness=50)\n",
    "        self.add_surface(\n",
    "            index=1,\n",
    "            thickness=7,\n",
    "            radius=43.7354,\n",
    "            is_stop=True,\n",
    "            material=\"N-SF11\",\n",
    "        )\n",
    "        self.add_surface(index=2, radius=-46.2795, thickness=50)\n",
    "        self.add_surface(index=3)\n",
    "\n",
    "        # add aperture\n",
    "        self.set_aperture(aperture_type=\"EPD\", value=25)\n",
    "\n",
    "        # add field\n",
    "        self.set_field_type(field_type=\"angle\")\n",
    "        self.add_field(y=0)\n",
    "        # self.add_field(y=3)\n",
    "\n",
    "        # add wavelength\n",
    "        self.add_wavelength(value=0.48613270)\n",
    "        self.add_wavelength(value=0.58756180, is_primary=True)\n",
    "        self.add_wavelength(value=0.65627250)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "lens1 = Singlet()\n",
    "lens2 = Singlet()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lens1.draw(num_rays=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lens_combined = lens1 + lens2  # lens1 + lens 1 is also possible\n",
    "lens_combined.draw(num_rays=5)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
